Problem: Olivia has a $20$ -meter-long fence that she plans to use to enclose a rectangular garden of width $w$. The fencing will be placed around all four sides of the garden so that its area is $18.75$ square meters. Write an equation in terms of $w$ that models the situation.
The strategy We know that the area of Olivia's garden must be $18.75$ square meters and that the perimeter of the garden must be $20$ meters (since this is the amount of fencing that she plans to use). If we let $w$ be the width of the garden and $l$ be the length of the garden, then we have $w\cdot l=18.75$ and $2w+2l=20$. If we can express one of these equations in terms of $w$ only, then we have the answer to the question. Expressing the length of the garden in terms of $w$ From the equation $w\cdot l=18.75$, it follows that $l=\dfrac{18.75}{w}$. Putting things together We found that $l=\dfrac{18.75}{w}$. Since $2w+2l=20$, we can substitute our expression in for $l$ and find an equation in terms of $w$ that models the situation. The answer is: $\begin{aligned}2w+2\left(\dfrac{18.75}{w}\right)&=20\\\\\\ 2w+\frac{37.5}{w}&=20\end{aligned}$ [Is there another way to do this problem?]